Pressure-sensitive adhesive tapes, which have traditionally been applied to moving webs, frequently adhere to adjacent layers of tape on tape-supply reels, making consistent and reliable unwinding difficult. One approach to solving this problem is to use heat-sensitive adhesive tape in lieu of the pressure-sensitive adhesive tape, since they do not adhere to adjacent layers unless heated. The high temperatures required to apply the tape, however, sometimes cause the tape or the web to which the tape is being applied to become overly softened, possibly losing their integrity and stretching or tearing during application of the tape. These problems are particularly aggravating in commercial-production scale apparatus for applying frontal diaper tapes to webs, both of which are relatively thin, because of the desirability of obtaining high production rates without sacrificing quality.